• 제목/요약/키워드: Constitutive Equation

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Constitutive Relation of Alloy Steels at High Temperatures

  • Lee, Young-Seog
    • International Journal of Precision Engineering and Manufacturing
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    • 제6권4호
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    • pp.55-59
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    • 2005
  • This paper presents a feasibility study whether Shida's constitutive equation being widely used for plain carbon steel in steel manufacturing industry can be extended to alloy steels with a due carbon equivalent model. T,he constitutive relation of the alloy steels (SAE9254, AISI52100 and AISI4140) is measured using hot deformation simulator (GLEEBLE 3500C) at high temperatures ($800^{\circ}C{\~}1000^{\circ}C$) within strain rates of $0.05{\~}40\;s^{-1}$. It has been found the predicted flow stress behavior (constitutive relation) of AISI52100 steel is in agreement with the measured one. On the other hand, the measured flow stress behavior of SAE9254 and AISI4140 steel partly concords with the predicted one when material experiences relatively high strain rate ($10{\~}40\;s^{-1}$) deformation at low temperature ($800^{\circ}C$). It can be deduced that, for AISI52100 steel, Shida's equation with the carbon equivalent model can be applicable directly to the roughing and intermediate finishing stand in hot rolling process for calculating the roll force and torque.

손상이 증가하는 아스팔트 콘크리트의 점탄성 구성모델 (Constitutive Modeling of Asphalt Concrete with Time-Dependent Damage Growth)

  • 이현종
    • 전산구조공학
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    • 제10권4호
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    • pp.229-238
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    • 1997
  • 본 논문에서는 반복하중에 의해 손상을 입은 아스팔트 콘크리트의 점탄성 구성모델에 대한 역학적 접근방법을 제시하였다. 모의변수로 나타낸 탄성-점탄성 일치원리는 아스팔트 콘크리트의 점탄성과 시간의존 손상의 증가를 별도로 평가하도록 적용되었다. 선형-점탄성 파괴역학에 사용되고 있는 미소균열의 증가법칙이 물체내 손상증가를 나타내는데 성공적으로 사용되었다. 응력과 모의변형도로 나타나는 구성방정식은 먼저 변형도조절에 대해 세워졌으며, 응력과 모의변형도를 모의응력과 변형도로 간단하게 대체함으로써 응력조절 구성방정식으로 변형되었다. 모의응력으로 나타낸 변형된 구성방정식은 응력조절모드에서 파괴에 이르는 아스팔트 콘크리트의 모든 역학적 거동을 충분히 예측하고 있다.

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충격량-운동량 이론을 접목시킨 발포 폴리프로필렌의 구성방정식 (A Constitutive Equation with Impulse-Momentum Theory for the Expanded Polypropylene)

  • 김병길;조재웅;정광영;김남훈;오범석;한영원;전성식
    • Composites Research
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    • 제29권3호
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    • pp.91-97
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    • 2016
  • 본 연구에서는 EPP(Expanded polypropylene) 준정적 및 충격 하중에 대한 구성방정식을 표현하는 데 있어서, 충격량-운동량 이론을 연계하였다. 또한, 구성방정식을 이루는 물리적으로 의미있는 변수들에 대해, 상대밀도의 함수로 표현하였다. 이를 위해, 연립 비선형 뉴튼-랩손 방법을 사용하여, 준정적 시험결과에 맞는 구성방정식의 변수값을 선정하였다. 또한, 충격량-운동량 이론이 구성방정식과 연계되어, 충격시 응력-변형률 선도를 변형률 속도에 따라 구하였고, 충격시험결과와 비교하였다. 향후에는 다른 재질의 발포고분자에도 본 구성방정식이 적용될 수 있을 것으로 사료된다.

이방성 손상모델을 이용한 콘크리트 구성방정식의 도출 (Constitutive Equation for Concrete using Anisotropic Continuum Damage Model)

  • 이기성;변근주
    • 대한토목학회논문집
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    • 제14권4호
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    • pp.751-759
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    • 1994
  • 콘크리트는 초기부터 미세균열을 포함하고 있으며 이들의 성장과 전파에 의해 파손이 발생한다. 이와같은 과정을 손상이라 한다. 연속체 손상역학의 개념을 소개하고 열역학 법칙으로부터 자유에너지함수와 소산포텐셜을 가정하여 이차텐서로 나타낸 손상모델의 전개법칙과 구성방정식을 제안하였다. 구성방정식은 탄성과 손상 및 소성을 고려하도록 하였다. 도출된 모델을 이용하여 단조하중에 의한 일축과 이축응력을 받는 콘크리트에 적용하여 그 타당성을 검정하였다.

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탄.소성 Work-Hardening 모델에 대한 Program 개발 -Lade 모델을 중심으로-

  • 박병기;정진섭
    • 한국지반공학회:학술대회논문집
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    • 한국지반공학회 1991년도 추계학술발표회 논문집 지반공학에서의 컴퓨터 활용 COMPUTER UTILIZATION IN GEOTECHNICAL ENGINEERING
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    • pp.255-270
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    • 1991
  • In recent years. finite element methods have been used with increasing effectiveness in analysis of displacements and stresses within soil masses. However, one of the weakest links in the analytical representations used in these methods is the models of the material behaviour. Herein is discribed a modification to the finite element methods that allows solution problems with realistic stress-strain relation for soils. A finite element program for the precision prediction of the stress distribution within foundation has been developed using the elasto-plastic Work-Hardening model. The developed program is verified by comparing the results of this study with the tested results for Sacramento river sand. The main results obtained from the numerical examples are as follows: The vertical total stress increments are insensitive to drainage and constitutive equation of materials. The horizontal total stress increments are considerably affected by the drainage and constitutive equation of materials. The maximum shear stresses are affected by the drainage only in elasto-ptastic meterirals. The excess pore water pressures and the volumetric strains not only are considerably affected by the constitutive equation of materials. but also have almost similar distribution.

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열탄소성 구성방정식 적분을 위한 새로운 알고리즘 (A New Algorithm for the Integration of Thermal-Elasto-Plastic Constitutive Equation)

  • 이동욱;신효철
    • 대한기계학회논문집
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    • 제18권6호
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    • pp.1455-1464
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    • 1994
  • A new and efficient algorithm for the integration of the thermal-elasto-plastic constitutive equation is proposed. While it falls into the category of the return mapping method, the algorithm adopts the three point approximation of plastic corrector within one time increment step. The results of its application to a von Mises-type thermal-elasto-plastic model with combined hardening and temperature-dependent material properties show that the accurate iso-error maps are obtained for both angular and radial errors. The accuracy achieved is because the predicted stress increment in a single step calculation follows the exact value closely not only at the end of the step but also through the whole path. Also, the comparison of the computational time for the new and other algorithms shows that the new one is very efficient.

알루미늄 합금박판 비등온 성형공정의 유한요소 해석 및 실험적 연구 (제2부:해석) (Finite Element Analysis and Experimental Investigation of Non-isothermal Forming Processes for Aluminum-Alloy Sheet Metals (Part2:Analysis))

  • 김성민;구본영;금영탁;김종호
    • 소성∙가공
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    • 제8권3호
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    • pp.252-261
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    • 1999
  • The 3-dimensional finite element program is developed to analyze the non-isothermal forming processes of aluminum-alloy sheet metals. Bishop's method is introduced to solve the heat balance and force equilibrium equations. Also, Barlat's non-quadratic anisotropic yield function depicts the planar anisotropy of the aluminum-alloy sheet. To find an appropriate constitutive equation, four different forms are reviewed. For the verification of the reliability of the developed program, the computational try-outs of the non-isothermal cylindrical cupping processes of AL5052-H32 and Al1050-H16 are carried out. As results, the constitutive equation relating to strain and strain-rate, in which the constants are represented by the 5th-degree polynomials of temperature, is in good agreement with measurement. The computational try-outs can predict optimal forming conditions in non-isothermal forming processes.

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동 하중에 대한 연강 재질의 변형율 속도 민감도 특성 연구 (Strain Rate Sensitive Behavior of Mild Steel Subjected to Dynamic Load)

  • 박종찬
    • 대한기계학회:학술대회논문집
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    • 대한기계학회 2004년도 추계학술대회
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    • pp.377-382
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    • 2004
  • The dynamic material characteristics on some mild steel sheets were observed. The dynamic tests were conducted on the ESH servo-hydraulic test machine. It was observed that the mechanical properties of mild steel are highly sensitive to the value of strain rate. The well known Cowper-Symonds constitutive equation was used to generalize the strain rate sensitivity effect. Modified constitutive equations were suggested to couple the strain hardening to the strain rate sensitivity. The dynamic stress-strain relationships for the mild steel sheets used in the present study were reasonably predicted using these modified constitutive equations.

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Plastic Deformation Behavior of Sintered Fe-Based Alloys for Light-Weight Automotive Components

  • Kang, Yohan;Yoon, Suchul;Kim, Minwook;Lee, Seok-Jae
    • Applied Science and Convergence Technology
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    • 제23권3호
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    • pp.151-159
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    • 2014
  • We investigated the effects of the chemical composition and the relative density on the plastic deformation behavior of sintered Fe-based alloys by means of compressive tests. Overall compressive stresses increased as the amount of alloying elements and the relative density were respectively increased. Addition of alloying elements except for Mo increased the yield stress regardless of the relative density. The relationship between the effects of the chemical composition and the relative density and the mean rate of the stress increase was analyzed. A constitutive equation based on the Ludwik equation with the regressed parameters was proposed to predict the compressive true stress-true strain curves of the sintered Fe-based alloys. The K and n values used in the proposed equation were regressed as a function of the alloying elements and the relative density based on the individual K and n values. The plastic deformation behavior predicted using the proposed constitutive equation showed reliable accuracy compared with experimental data.